Problem: Solve for $x$. Enter the solutions from least to greatest. $(x -7)(-4x -2)=0$ $\text{lesser }x = $
Answer: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(x -7)(-4x -2)=0$. So either $(x -7)=0$ or $(-4x -2)=0$ : $\begin{aligned} (1)&&x -7&=0 \\\\ &&x&=7 \end{aligned}$ $\begin{aligned} (2)&&-4x -2&=0 \\\\ &&-4x &= 2 \\\\ &&x&=-\dfrac{1}{2} \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -\dfrac{1}{2} \\\\ \text{greater } x &= 7 \end{aligned}$